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Let P be a point equidistant from two intersecting lines L and M at a point A. then,
Option: 1
the line AP bisects the angle between L and M.

Option: 2
the line L bisects the angle between AP and M.

Option: 3
the line M bisects the angle between AP and L.

Option: 4
None of the above

Answers (1)

best_answer

$\begin{align*} &\text{In } \triangle PAM \text{ and } \triangle PAN, \text{ we have:} \\ &\angle PMA = \angle PNA = 90^{\circ} \\ &PM = PN \quad \text{(given)} \\ &AP = AP \quad \text{(common)} \\ \therefore &\triangle PAM \cong \triangle PAN \quad \text{(by RHS-criteria)} \\ \therefore &\angle PAM = \angle PAN \quad \text{(c.p.c.t.)} \\ &\text{Hence, the line AP bisects the angle between L and m.} \end{align*}$

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Ritika Kankaria

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